Question: Simplify the following expression and state the condition under which the simplification is valid: $r = \dfrac{n^2 - 13n + 30}{n^2 - 5n + 6}$
Answer: First factor the expressions in the numerator and denominator. $ \dfrac{n^2 - 13n + 30}{n^2 - 5n + 6} = \dfrac{(n - 10)(n - 3)}{(n - 2)(n - 3)} $ Notice that the term $(n - 3)$ appears in both the numerator and denominator. Dividing both the numerator and denominator by $(n - 3)$ gives: $r = \dfrac{n - 10}{n - 2}$ Since we divided by $(n - 3)$, $n \neq 3$. $r = \dfrac{n - 10}{n - 2}; \space n \neq 3$